Minds On

Writing equations

There are four mathematical symbols that indicate inequality. An arrow pointing to the right means greater than. An arrow pointing to the right with a line below it means greater than or equal to. An arrow pointing to the left means less than. An arrow pointing to the left with a line below it means less than or equal to.

Record the following statements algebraically using a method of your choice.

  1. The sum of 6 and an unknown number is less than 17.
  2. The difference between a number and 8 is greater than 13.
  3. The product of 5 and a number is less than 32.5.
  4. A number divided by 4 is less than or equal to 3.

If there is an equal sign instead of the “less than” or “greater than” how can you solve each equation?

How could we record the solution to the original inequality on a number line?

  • The sum of 6 and an unknown number is less than 17.

What is important to indicate on the number line so the statement is still true?

Press ‘Answer’ to reveal the answer to the problem.

6 + x < 17

x < 11

A number line with an open circle above the number 11 and a line with an arrow extending past number 2.

Number line from 2-20. Open dot over 11 with line over the numbers to the left and an arrow pointing to the left.

It is important that the dot over 11 is open because x cannot be 11. 11 isn't included in the possible solutions.

Action

Task 1: Graphing inequalities on a number line

Consider the inequalities from the Minds On section. How would we display the solutions on a number line?

  1. The difference between a number and 8 is greater than 13.
    First record the statement as an expression.
    N − 8 > 13
    Then solve as though there were an equal sign instead of a greater than sign.
    N − 8 = 13
    N = 21
    To keep the original inequality true, we know that n has to be bigger than 21. On a number line, we would use an open dot to show that 21 is not included, but everything else larger than 21 could be included.
A number line with a circle around the number 21 and a line with an arrow extending to number 30.

Your turn

2. Graph the solutions to the inequalities on a number line.

  1. The product of 5 and a number is less than 32.5.
  2. A number divided by 4 is less than or equal to 3.

Press ‘Answer’ to reveal the solutions to the inequalities.

  1. a.
    5n < 32.5
    n < 32.5 ÷ 5
    n < 6.5
    A number line with a closed circle above the number 6.5 and a line with an arrow extending to number 3.
    b.
    n ÷ 4 ≤ 3
    n ≤ 3 × 4
    n ≤ 12
    A number line with a closed circle above the number 12 and a line with an arrow extending to number 5.

Task 2: A four-day getaway

  1. A photographer is saving for a photo shoot. They need at least $500 to spend on equipment. They can put aside $25 a week. How many weeks will it take the photographer to have enough for their photo shoot?
    Create an equation to solve the inequality.
    Use a number line, t-table, or other method of choice to show the increase in savings per week.
    Record digitally, orally, or in print, or create a detailed description about the amount saved and the length of time.
  2. An accountant has $750 in a bank account when they left for a 4-day conference. They plan to have no less than $150 in the account by the end of the conference. What is the maximum amount that can be spent per day at the conference?
    Create an equation to solve the problem.
    On day 2 the accountant spent double what they spent on day 1, and on day 3 and 4 they spent half of what they spent on day 1.
    How much did the accountant spend on each day?
    Record your thoughts digitally, orally, or in print, or create a detailed description about the amount spent on the different days.

Consolidation

At the bowling alley

A bowling league charges $10 to join and $5 per game. A bowler paid more than $25 last week to bowl. How many games could they have played?

Player A said they could play exactly three games.

Player B said they could play more than three games.

Which bowler is correct?

How do you know? Justify your answer by showing your work.

Record your responses digitally, orally, or in print.

Think about your learning

  1. How are equations and inequalities similar?
  2. How are equations and inequalities different?
  3. What is important to remember when representing solutions to equalities and inequalities on a number line?

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

I feel...

Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.

When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.